Anisotropic surface measures as limits of volume fractions (Q1713248)

The new characterization of the perimeter of a measurable set in \(\mathbb R^n\) due to [the first author et al., Commun. Pure Appl. Math. 69, No. 6, 1062--1086 (2016; Zbl 1352.46026)] is considered in the paper. Their approach is modified by using covering families made by translations of a given open bounded set with Lipschitz boundary. The main result is Theorem 1 formulated in the Introduction. It is proved in Section 3 by a simple comparison argument based on the results of [loc. cit.]. The proof is technical and interesting. Few examples on coverings and estimates are given in Section 4. For the entire collection see [Zbl 1403.46004].